A few things can happen if you don’t show up for your Family Court case.
If you’re the petitioner, your case will probably be dismissed, if you have not notified the court and told them why you are not there. If your case is dismissed, you can usually file it again.
If you are lucky, the court may adjourn the case to another day. You probably won’t get a second chance, though.
If you are the respondent, the court may proceed without you. This could mean that the court will hold a hearing, and the petitioner will likely win the case. If this happens, you can try to vacate the default judgment, but you need legal grounds.
In certain cases, such as child support, child neglect, juvenile delinquency, and cases where the safety of a child is in question, the court may issue an arrest warrant for you.
All in all, it is usually not a good idea to miss your Family Court case. If you have no choice, be sure to tell the court or your lawyer.